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The notion of dependence occurs naturally in many areas of mathematics: for example, graph theory, linear algebra, and the study of field extensions. These apparently quite different concepts share certain properties. Matroids are the axiomatic mathematical objects that arise from these common properties, in the same way that groups are the objects we discover when we consider the abstract properties of symmetries. MATH432 is an introduction to structural matroid theory, including the basic definitions and results, and excluded-minor characterizations of several classes of matroids. If time allows we will consider one of the highlights of the subject: Seymour’s decomposition theorem for regular matroids.
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Year2010
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